A386475 Least prime starting a run of exactly n consecutive primes with identical counts of odd digits.

2, 5, 3, 11, 97, 503, 499, 491, 14303, 14293, 157259, 157253, 1525723, 4576997, 4576993, 4576991, 10411013, 33388093, 188332121, 194259301, 2853982501, 2853982499, 2853982477, 3913474277, 10883385143, 22809734971, 34883348389, 34883348369, 34883348341

Offset

1,1

Comments

Consecutive previous primes of the selected prime are ignored even though the may also have an identical count of digits.

Links

Table of n, a(n) for n=1..29.

Example

a(2) = 5, because the two primes in the sequence starting at 5, namely 5 and 7, each contain the same number of odd digits, and no earlier prime sequence meets this criterion.
In [2], each number contains 0 odd digits.
In [5, 7], each number contains 1 odd digit.
In [3, 5, 7], each number contains 1 odd digit.
In [11, 13, 17, 19], each number contains 2 odd digits.
In [97, 101, 103, 107, 109], each number contains 2 odd digits.
In [503, 509, 521, 523, 541, 547], each number contains 2 odd digits.
In [499, 503, 509, 521, 523, 541, 547], each number contains 2 odd digits.
In [491, 499, 503, 509, 521, 523, 541, 547], each number contains 2 odd digits.
In [14303, 14321, 14323, 14327, 14341, 14347, 14369, 14387, 14389], each number contains 3 odd digits.
In [14293, 14303, 14321, 14323, 14327, 14341, 14347, 14369, 14387, 14389], each number contains 3 odd digits.

Mathematica

oddn[n_] := Plus @@ Mod[IntegerDigits@ n, 2]; T = Table[0, {99}]; p = 1; While[p < 2  10^6, p = NextPrime[p]; c = oddn[p]; r=1; q=p; While[True, q = NextPrime[q]; If[oddn[q] == c, r++, Break[]]]; If[T[[r]] == 0, T[[r]] = p]]; Take[T, Position[T, 0][[1, 1]] - 1] (* Giovanni Resta, Jul 23 2025 *)

Crossrefs

Cf. A000040, A196564,

Sequence in context: A225258 A162613 A120858 * A124937 A279342 A169852

Adjacent sequences: A386472 A386473 A386474 * A386476 A386477 A386478

Keyword

nonn,base

Author

Jean-Marc Rebert, Jul 23 2025

Extensions

More terms from Giovanni Resta, Jul 23 2025

Status

approved